8 Time series functional forms Logarithmic form Suppose an a

8. Time series functional forms: Logarithmic form Suppose an annual, time series data set for the years 1950 through 1987 was analyzed using OLS to examine the relationship between U.S. minimum wage levels and employment in Puerto Rico. The regression results are as follows, with standard errors in parentheses: logl prepop)1300 logf minicov)-003 logf usgnp) (0.53) (0.07) where prepopt = employment rate in Puerto Rico during year t usgnp,real U.S. gross national product (in billions of dollars) in year t mincova measure of the importance of the minimum wage relative to average wages R2 0.610 R0.599

Solution

A cross-sectional data is collected at a given point in time and time series data is collected over a period of time. Sometimes both are used together to derive certain results. The explanatory variables in the cross-section analysis can be those that vary in a cross-section and over time or alternatively one of them but time series analysis has certain constraints. Hence a cross-sectional data is more general and can be applied to time series with different functional forms and here the form is linear as it is a logarithmic transformation.

the correct option is TRUE

the estimated elasticity of the employment rate with respect to the variable mincov is -0.194 as the slope estimates of a logarithmic regression equation gives the elasticity of the dependent variable with respect to the explanatory variable.

the t statistic for slope coefficient is calculated as -0.194/0.07 = -2.77 which is different from how the t statistic would be calculated for cross-sectional data.